Unit IV

The Theory of the Firm

• This chapter is the first of four exploring the theory of the firm.

• A firm (or producer or business) combines inputs — labor, capital, land, and materials — to produce outputs.

  • If the firm is successful, the outputs are more valuable than the inputs.
    
  • Production includes more than just manufacturing — encompassing any process or service that creates value, such as transportation, distribution, and retail.

Key Decisions in Production

• Production involves several important decisions that define a firm’s behavior, including:
  • What product or products should the firm produce?
    
  • How should the firm produce them?
    
  • How much output should the firm produce?
    
  • What price should the firm charge for its products?
    
  • How much labor should the firm employ?

Determinants of Firm Behavior

• The answers to these questions depend on both production and cost conditions and on the market structure of the industry.

• Market structure refers to how competitive an industry is and can be described by questions such as:

  • How much market power does each firm possess?
    
  • How similar are products across firms?
    
  • How difficult is it for new firms to enter the industry?
    
  • Do firms compete primarily on price, advertising, or other product differences?

Spectrum of Competition

Range in Size of U.S. Firms

Source: U.S. Census, 2010

Profit and Cost Basics

• Each business, regardless of size or complexity, tries to earn a profit:
  • \(\pi = \text{Revenue} - \text{Costs}\)
  • \(\text{Revenue} = TR = P \times Q = \text{Price} \times \text{Quantity}\)
  • \(\text{Costs} = TC = FC + VC + OC = \text{Fixed} + \text{Variable} + \text{Opp.}\)

Explicit vs. Implicit Costs

• Explicit costs are out-of-pocket expenses made by the firm.
  • Examples include wages paid to employees or rent for office space.
• Implicit costs represent the opportunity cost of using resources the firm already owns.
  • Examples include working in the business without a formal salary, or using part of a home as retail space.
    
  • Implicit costs also include depreciation of equipment and materials necessary for production.

Fixed and Variable Inputs

• Fixed inputs are those that cannot easily be changed in the short run.
  • For example, a building is a fixed input — the owner is bound by the lease until it expires.
• Variable inputs can be increased or decreased easily in the short run.
  • For instance, a pizzeria can order more ingredients or hire another worker with little delay.

Time Horizons

• The short run is the period during which at least one factor of production is fixed.
  • During a lease, the pizza shop operates in the short run because it cannot change its building size.
• The long run is the period during which all factors are variable.
  • Once the lease expires, the owner can relocate to a larger or smaller space.

Accounting vs. Economic Profit

• Accounting profit is a cash-based measure:
  • Total revenue minus explicit costs — the difference between money received and money paid out.
• Economic profit equals total revenue minus total cost, including both explicit and implicit costs.
  • This distinction matters because firms pay taxes (and dividends) on accounting profit, but the efficiency of decisions depends on economic profit.

Accounting vs. Economic Profit Example

• Eryn currently works for a corporate law firm where she makes $125k and is considering opening her own legal practice.
  • She expects to earn $200k per year once she establishes herself.
  • To run her own firm, she would need an office and a law clerk.
  • Office rent: $50k/year; law clerk: $35k/year
• Accounting \(\pi = \text{TR} - \text{EC} = \$200 - (\$50k + \$35k) = \$115k\)
• Economic \(\pi = \text{TR} - \text{EC} - \text{OC} = \$200 - (\$50k + \$35k) - \$125k = -\$10k\)

Production Functions

• Recall our factors of production are: \(Q(N,L,K,E) = f(N,L,K,E)\)

• Often times, we simplify the production function such that \(Q(K,L)\)

• The marginal product of labor (capital) measures how much additional output one more worker (piece of technology) would increase a firm’s output, holding all else constant.

  • \(MP_L = \frac{\partial Q(K,L)}{\partial L} \approx \frac{\Delta Q}{\Delta L}\)

Production Schedule: Example

Production Schedule: Example

Production Schedule: Example

The Law of Diminishing Marginal Product

• As more workers are added, marginal product may increase at first — due to specialization or efficiency gains — but eventually decreases as inputs become crowded or less productive.
  • In some cases, adding more workers may have no effect or even a negative effect on total output.
• This pattern is known as the Law of Diminishing Marginal Product, a key feature of short-run production.
  • The idea parallels diminishing marginal utility in consumer theory.

Cost Relationships

• \(\text{Average Cost} = \dfrac{TC}{Q} = \dfrac{VC + FC}{Q}\)

• \(\text{Marginal Cost} = \dfrac{\Delta TC}{\Delta Q} = \dfrac{\Delta VC + \Delta FC}{\Delta Q} = \dfrac{\Delta VC}{\Delta Q} = \dfrac{VC_2 - VC_1}{Q_2 - Q_1}\)

Cost Curve Example

Cost Schedule Example

z <- data.frame(
  labor = 0:7,
  quantity = c(0, 16, 40, 60, 72, 80, 84, 82),
  fixed_cost = 160,
  variable_cost = 0:7 * 80
)
z$total_cost <- z$fixed_cost + z$variable_cost
z

  labor quantity fixed_cost variable_cost total_cost
1     0        0        160             0        160
2     1       16        160            80        240
3     2       40        160           160        320
4     3       60        160           240        400
5     4       72        160           320        480
6     5       80        160           400        560
7     6       84        160           480        640
8     7       82        160           560        720

Cost Schedule Example

z$average_cost <- z$total_cost / z$quantity
z$marginal_cost <- NA
z$marginal_cost[2:nrow(z)] <- diff(z$total_cost) / diff(z$quantity)
z

  labor quantity fixed_cost variable_cost total_cost average_cost marginal_cost
1     0        0        160             0        160          Inf            NA
2     1       16        160            80        240    15.000000      5.000000
3     2       40        160           160        320     8.000000      3.333333
4     3       60        160           240        400     6.666667      4.000000
5     4       72        160           320        480     6.666667      6.666667
6     5       80        160           400        560     7.000000     10.000000
7     6       84        160           480        640     7.619048     20.000000
8     7       82        160           560        720     8.780488    -40.000000

Cost Curves Example

Cost Schedule Example

Change in cost per worker

z$average_cost <- z$total_cost / z$labor
z$marginal_cost <- NA
z$marginal_cost[2:nrow(z)] <- diff(z$total_cost) / diff(z$labor)
z

  labor quantity fixed_cost variable_cost total_cost average_cost marginal_cost
1     0        0        160             0        160          Inf            NA
2     1       16        160            80        240     240.0000            80
3     2       40        160           160        320     160.0000            80
4     3       60        160           240        400     133.3333            80
5     4       72        160           320        480     120.0000            80
6     5       80        160           400        560     112.0000            80
7     6       84        160           480        640     106.6667            80
8     7       82        160           560        720     102.8571            80

Cost Curves Example

Change in cost per worker

Output Schedule Example

## made up data, workers and a production function
z <- data.frame(l = 1:100)
z$q <- 2*log(z$l + 4) + 2*log(max(z$l)) + 1 - 2*log(max(z$l) + 4)
z <- rbind(data.frame(l = 0, q = 0), z)

# marginal product of labor
z$mp_l <- NA
z$mp_l[2:nrow(z)] <- diff(z$q) / diff(z$l)

head(round(z, 1))

  l   q mp_l
1 0 0.0   NA
2 1 4.1  4.1
3 2 4.5  0.4
4 3 4.8  0.3
5 4 5.1  0.3
6 5 5.3  0.2

Output Curves Example

Output Schedule Example

# costs (variable + fixed)
wage <- 10
z$total_cost <- z$l * wage + 1000
z$average_cost <- z$total_cost / z$q

# Marginal cost via discrete differences
z$marginal_cost <- z$total_cost / z$q
z$marginal_cost[2:nrow(z)] <- diff(z$total_cost) / diff(z$q)

## peak at the data
head(round(z, 1))

  l   q mp_l total_cost average_cost marginal_cost
1 0 0.0   NA       1000          Inf           Inf
2 1 4.1  4.1       1010        243.9           2.4
3 2 4.5  0.4       1020        226.4          27.4
4 3 4.8  0.3       1030        214.0          32.4
5 4 5.1  0.3       1040        204.7          37.4
6 5 5.3  0.2       1050        197.5          42.5

Cost Curves Example #2

Output Schedule Example

Change in cost per worker

# costs (variable + fixed)
wage <- 10
z$total_cost <- z$l * wage + 1000
z$average_cost <- z$total_cost / z$l

# Marginal cost via discrete differences
z$marginal_cost <- z$total_cost / z$l
z$marginal_cost[2:nrow(z)] <- diff(z$total_cost) / diff(z$l)

## peak at the data
head(round(z, 1))

  l   q mp_l total_cost average_cost marginal_cost
1 0 0.0   NA       1000          Inf           Inf
2 1 4.1  4.1       1010       1010.0            10
3 2 4.5  0.4       1020        510.0            10
4 3 4.8  0.3       1030        343.3            10
5 4 5.1  0.3       1040        260.0            10
6 5 5.3  0.2       1050        210.0            10

Cost Curves Example #2

Change in cost per worker

Profit Margin

• \(\text{Average } \pi = \dfrac{\pi}{Q} = \dfrac{TR - TC}{Q} = \dfrac{TR}{Q} - \dfrac{TC}{Q}=...\)

• \(...=\dfrac{TR}{Q} - \dfrac{TC}{Q} = \dfrac{P \times Q}{Q} - \dfrac{AC \times Q}{Q} = P - AC\)

• \(\text{Average } \pi = P - AC\)

• Average profit is also known as the profit margin or profit per unit

  • If \(P > AV\), then the firm is profitable
  • If \(P > MC\), then increasing production will increase profits

Production in the Long Run

• The long run refers to a time horizon in which the firm has no fixed inputs — all factors of production can be adjusted.
  • In contrast, in the short run, capital is typically treated as fixed, while labor is variable.
• The long run is not a specific length of time; it depends on the nature of the firm.
  • For example, if a firm has a one-year lease on its factory, then the long run begins after that lease expires, since the firm can now change its facility.
    
  • In the long run, a firm can build new factories, purchase new machinery, or close existing facilities.

Production in the Long Run

Production in the Long Run

• In planning for the long run, a firm compares alternative production technologies (or processes).
  

• Technology refers to all possible methods of combining inputs to produce outputs — it does not necessarily mean a new invention.

• Firms are assumed to seek the lowest-cost technology capable of producing a desired level of output.

Choice of Production Technology

Choice of Production Technology

Costs in the Long Run

Introduction to Perfect Competition

• Did you ever babysit, deliver newspapers, or mow lawns for money?
  • If so, you probably faced many competitors offering identical services.
    
  • There was nothing preventing others from entering the market, and most of you charged the going rate.
    
  • If you tried to charge more, customers could simply turn to someone else.

Introduction to Perfect Competition

• A perfectly competitive market is an idealized case—but some industries come close.
• Firms in these markets face many competitors selling nearly identical goods and must act as price takers.
• Economists often use agricultural markets as a classic example.

Perfect Competition

Core Idea

• A perfectly competitive firm is a price taker because intense competition forces it to accept the market equilibrium price.
  • If a firm raises its price even slightly, it will lose all sales to competitors.
• The market supply and demand together determine price — not the actions of any single firm.
• Each firm is such a small part of the overall market that changing its own output does not affect the market price.

Perfect Competition

Key Conditions

• Firms operate under perfect competition when the following hold:
  • Many firms produce identical products.
    
  • Many buyers and sellers participate in the market.
    
  • Full information exists—buyers and sellers know all relevant details.
    
  • Free entry and exit—firms can enter or leave the market without barriers.

Perfect Competition

Profit Maximization

A perfectly competitive firm has one major decision to make: how much to produce.

Profit is defined as:

\[ \pi = TR - TC = P \times Q - AC \times Q = (P - AC)Q \]

Perfect Competition

Profit Maximization

• Because the firm must accept the market price, it cannot set its own.
  • It can sell any quantity at that price, meaning it faces a perfectly elastic demand curve.
• When the firm chooses its output level, this quantity (combined with market prices for output and inputs) determines its total revenue, total costs, and therefore profit.

Perfect Competition

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Profit

Perfect Competition

Break-even

Perfect Competition

Loss

Perfect Competition

Entry and Exit

• Firms enter or exit the market in response to profit opportunities.
  
• While no individual firm can influence the market price, the collective entry or exit of many firms affects overall market supply.
  • A change in total market supply shifts the market price, which in turn alters profitability for all firms.

Perfect Competition

Long-Run Equilibrium

• When profits exist, new firms enter — like sharks drawn to blood — increasing market supply and driving prices down.
  • This process continues until prices fall to the point where \(P = AC \implies \pi = 0\)
• In long-run equilibrium, no firm has an incentive to enter or exit.
  • All firms earn zero economic profit and produce where \(P = MR = MC = AC\) since MC intersects AC at its minimum point.

Perfect Competition

Long-Run Adjustment

• In the short run, firms may earn profits or losses.
  • Profits attract entry, pushing prices down to the zero-profit level.
    
  • Losses lead to exit, reducing supply and pushing prices up to the zero-profit level.
• In the long run, all firms that remain operate at the lowest possible cost with \(\pi = 0\) ensuring no incentive to enter or leave the market.

Perfect Competition

Long-run Equilibirum

Monopoly

Introduction

• A monopoly is a market with no competition, giving the firm substantial market power.
  • A single firm produces all output in the market.
    
  • Since it faces no direct rivals, it can set prices subject only to the demand curve.
• Although a monopoly strictly means one producer, the term is often used more loosely to describe markets dominated by a single firm with very high market share.

Monopoly

Market Share

• A firm is considered a monopoly when it produces a product with no close substitutes.
  • If consumers can choose among several similar alternatives, even if not identical, the market is not truly monopolized.
    
  • However, determining what counts as a close substitute is often subjective and debated, making the boundaries of monopoly power difficult to define in practice.

Monopoly

Barriers to Entry

• Because monopolies face no competition, they can earn sustained economic profits.
  • In a competitive market, such profits would attract entry—but monopolies persist because of barriers to entry.
• Barriers to entry are legal, technological, or market conditions that prevent or discourage potential competitors.
  • These barriers can range from modest (e.g., high startup costs) to extreme (e.g., exclusive control of scarce resources).
    
  • For instance, only a limited number of radio frequencies exist; once a firm owns all of them, new entrants are effectively blocked.

Monopoly

Monopoly

Natural Monopoly

• A natural monopoly arises when economies of scale are large relative to market demand.
  • Once the fixed costs of infrastructure are in place, the marginal cost of serving additional customers is very low.
    
  • As a result, one firm can produce the entire market output more efficiently than several smaller firms duplicating investments.

Monopoly

Natural Monopoly: Examples

• Once a water utility installs main pipes, the cost of connecting one more home is minimal.
  
• Similarly, after an electric company installs lines, serving additional homes is cheap.
  
• A second firm entering either market would have to duplicate infrastructure—an inefficient use of resources.

Monopoly

Local Market Example

• Natural monopolies can also occur in smaller regional markets where products are costly to transport.
  • For example, cement plants experience economies of scale, but transporting cement long distances is expensive.
    
  • In areas without access to water transport, a single cement plant may efficiently serve the entire local market.

Monopoly

Natural Monopoly

Monopoly

Economies of Scale and Market Size

• Economies of scale combined with market size can naturally restrict competition.
  
• The long-run average cost (LRAC) curve for airplane manufacturing:
  • Shows economies of scale up to about 8,000 planes per year at price \(P_0\)
    
  • Then constant returns to scale from 8,000–20,000 planes
    
  • And diseconomies of scale beyond 20,000 planes

Monopoly

Natural Monopoly

• The market demand curve intersects the LRAC at about 5,000 planes per year and a price \(P_1 > P_0\).
  • This means the market can support only one efficient producer.
    
  • If a second firm entered producing 4,000 planes, its average cost would exceed that of the incumbent—making it uncompetitive.
    
  • If it entered at 8,000 planes to lower costs, it would face insufficient demand to sell its output.

Monopoly

Promoting Innovation

• Suppose a company invests heavily in research and development and discovers a cure for the common cold.
  • In a world where information spreads instantly, other firms could copy the formula and sell the same drug at a lower price—since they didn’t bear the R&D costs.
    
  • If this happened, few firms would have an incentive to invest in research, leading to less innovation overall.
• Intellectual property law grants creators temporary or exclusive rights over their ideas, inventions, and brands—providing incentives for innovation while eventually allowing competition.

Monopoly

Legal Monopolies & Intellectual Property

• Patents give inventors the exclusive right to make, use, or sell an invention (usually 20 years) so they can recover R&D costs before rivals enter the market.
  
• Trademarks protect distinctive names or symbols that identify products—like Chiquita, Chevrolet, or the Nike swoosh.
  
• Copyrights safeguard original works such as books, music, and art for the author’s life plus 70 years.
  
• Trade secrets protect confidential business information—like the Coca-Cola formula—without requiring public disclosure.

Monopoly

Deregulation

• For decades, some monopolies were legally protected due to technological or logistical limits.
  • For example, AT&T was once the only company allowed to provide both local and long-distance telephone service.
    
  • From the 1930s to 1970s, federal regulations also restricted airline routes and fares, bank interest rates, and trucking prices.
  • As technology evolved, these monopolies became harder to justify.

Monopoly

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Monopoly

Allocative Efficiency

• While monopolies are often criticized for charging high prices, economists focus on their failure to produce the socially optimal quantity of output.
  • Unlike perfectly competitive markets, monopolies restrict production to maximize profit, leading to allocative inefficiency—too little output from society’s perspective.
• Allocative efficiency occurs when the marginal benefit to society from one more unit of a good equals its marginal cost, ensuring that resources are used where they generate the greatest overall value.

Imperfect Competition

• Most real-world firms operate between the extremes of perfect competition and monopoly.
  • These firms face some market power — they can influence the price they charge — but not complete control.
• Their behavior depends on how many competitors exist and how differentiated their products are.

Imperfect Competition

Monopolistic Competition

• A monopolistically competitive market features many firms competing to sell products that are similar but not identical.
  • Each firm offers a distinctive product, giving it some control over price.
  • Examples include clothing retailers, restaurants, grocery stores, or even products like golf balls and beer, which differ through branding, advertising, and consumer perception.
• Monopolistic competition blends features of both competition and monopoly - many sellers, but each with a mini-monopoly over its own variety.

Imperfect Competition

Oligopoly

• An oligopoly is a market dominated by a small number of large firms.
  • Example: Boeing and Airbus together produce nearly all large commercial aircraft worldwide.
    
  • Example: The soft drink industry, led by Coca-Cola and Pepsi.
• Key features:
  • High barriers to entry
    
  • Strategic interdependence — firms consider how rivals will react to their output and pricing decisions.

Imperfect Competition

Differentiated Products

• Product differentiation can occur through:
  • Physical features: e.g., nonstick coating, extra spicy flavor, redesigned for comfort
    
  • Location: proximity to consumers or key suppliers (e.g., a gas station at a busy intersection)
    
  • Intangible aspects: guarantees, reputation, free delivery, financing options
    
  • Perception: branding and advertising create psychological differences among otherwise similar products

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Entry and Exit

Imperfect Competition

Increased Competition (p - 2)

Imperfect Competition

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Monopolistic Competition and Efficiency

• In perfect competition, entry and exit push firms to produce at the minimum of AC, achieving productive efficiency.

• In monopolistic competition, entry and exit lead firms to produce on the downward-sloping portion of the AC curve (not at its minimum) so the market is not productively efficient.

Imperfect Competition

Monopolistic Competition and Efficiency

• Perfectly competitive firms produce where P = MC, achieving allocative efficiency.

• Monopolistically competitive firms set MR = MC, but because demand slopes downward, P > MR, meaning P > MC.

  • When P > MC, society values extra units more than they cost to produce, but the firm does not supply them.
  • The result is allocative inefficiency – a higher price and lower quantity than under perfect competition.

Imperfect Competition

Benefits of Variety and Differentiation

• Although monopolistic competition lacks productive and allocative efficiency, it provides variety.
  • Consumers prefer differentiated options (different clothes, foods, services, and product features) over the uniformity implied by perfect competition.
  • Firms compete through service, quality, features, and innovation.

Imperfect Competition

Benefits of Variety and Differentiation

• Debate persists over whether markets create too much or the right amount of variety.
  • Critics argue that extensive differentiation and advertising can be socially wasteful.
    
  • Defenders argue that consumers choose variety, and firms’ pursuit of profit drives meaningful innovation and choice.
• The “optimal” amount of variety is hard to define and depends on how one values consumer choice.

Imperfect Competition

Oligopoly

• Oligopoly firms face a strong temptation to act like a monopoly.
  • By coordinating, they can restrict output, raise prices, and share the resulting profits.
    
  • Such coordinated behavior is called collusion.
• A formal collusive agreement to set output and price like a monopoly is known as a cartel.

Imperfect Competition

Game Theory

• Oligopolies are mutually interdependent, so no single unified theory predicts their behavior.

• Economists instead use game theory, which studies strategic decision-making where payoffs depend on others’ actions.

  • Game theory has broad applications in economics, business, law, and military strategy.

Imperfect Competition

Prisoner’s Dilemma

• The prisoner’s dilemma illustrates situations where cooperation yields higher gains than acting in self-interest.
  • It maps well onto oligopoly: firms would benefit from cooperating, but each has an incentive to cheat.
• The term comes from a classic scenario in economics and the social sciences, referring to scenarios where individuals are “prisoner” to their own best strategy.

Imperfect Competition

Prisoner’s Dilemma

Imperfect Competition

Prisoner’s Dilemma

Imperfect Competition

Oligopoly

• When Oligopoly arises from innovation or economies of scale, it can benefit consumers by lowering costs or improving products.

• However, strong barriers to entry allow oligopolists to earn long-run profits and reduce pressure to innovate or provide high-quality service.

  • Oligopolists also tend not to produce at the minimum of AC.

• The goal of eocnomic policy is to balance these realities.